New Equations Go Beyond Einstein’s Theory of General Relativity

Quantum Transfiguration of Kruskal Black Holes

Artist depiction of loop quantum gravity effects in a black hole. The bottom half of the image depicts the black hole which, according to general relativity, traps everything including light. Loop quantum gravity, a theory that extends Einstein’s general relativity using quantum mechanics, overcomes this tremendous pull and liberates everything shown in the top half of image, thus solving the fundamental problem of black hole singularity. Photo Credit: A. Corichi and J. P. Ruiz.

When stars collapse, they can create black holes, which are everywhere throughout the universe and therefore important to be studied. Black holes are mysterious objects with an outer edge called an event horizon, which traps everything including light. Einstein’s theory of general relativity predicted that once an object falls inside an event horizon, it ends up at the center of the black hole called a singularity where it is completely crushed. At this point of singularity, gravitational attraction is infinite and all known laws of physics break down including Einstein’s theory. Theoretical physicists have been questioning if singularities really exist through complex mathematical equations over the past several decades with little success until now. LSU Department of Physics & Astronomy Associate Professor Parampreet Singh and collaborators LSU Postdoctoral Researcher Javier Olmedo and Abhay Ashtekar, the Eberly Professor of Physics at Penn State developed new mathematical equations that go beyond Einstein’s theory of general relativity overcoming its key limitation—the central singularity of black holes. This research was published recently in Physical Review Letters and Physical Review D and was highlighted by the editors of the American Physical Society.

Theoretical physicists developed a theory called loop quantum gravity in the 1990s that marries the laws of microscopic physics, or quantum mechanics, with gravity, which explains the dynamics of space and time. Ashtekar, Olmedos and Singh’s new equations describe black holes in loop quantum gravity and showed that black hole singularity does not exist.

“In Einstein’s theory, space-time is a fabric that can be divided as small as we want. This is essentially the cause of the singularity where the gravitational field becomes infinite. In loop quantum gravity, the fabric of space-time has a tile-like structure, which cannot be divided beyond the smallest tile. My colleagues and I have shown that this is the case inside black holes and therefore there is no singularity,” Singh said.

Instead of singularity, loop quantum gravity predicts a funnel to another branch of the space-time.

“These tile-like units of geometry—called ‘quantum excitations’— which resolve the singularity problem are orders of magnitude smaller than we can detect with today’s technology, but we have precise mathematical equations that predict their behavior,” said Ashtekar, who is one of the founding fathers of loop quantum gravity.

“At LSU, we have been developing state-of-the-art computational techniques to extract physical consequences of these physical equations using supercomputers, bringing us closer to reliably test quantum gravity,” Singh said.

Einstein’s theory fails not only at the center of the black holes but also to explain how the universe was created from the Big Bang singularity. Therefore, a decade ago, Ashtekar, Singh and collaborators began to extend physics beyond the Big Bang and make new predictions using loop quantum gravity. Using the mathematical equations and computational techniques of loop quantum gravity, they showed that the Big Bang is replaced by the “Big Bounce.” But, the problem of overcoming black hole singularity is exceptionally complex.

“The fate of black holes in a quantum theory of gravity is, in my view, the most important problem in theoretical physics,” said Jorge Pullin, the Horace Hearne professor of theoretical physics at LSU, who was not part of this study.

The research was supported by the U.S. National Science Foundation, the Urania Stott Fund of the Pittsburgh Foundation, the Penn State Eberly College of Science and the Ministry of Economy and Competitiveness, or MINECO, in Spain.


67 Comments on "New Equations Go Beyond Einstein’s Theory of General Relativity"

  1. Abhash Kumar singh | December 21, 2018 at 10:55 pm | Reply

    If v>=10c,then we can pass the black hole.

  2. Science achieved many breakthroughs this year, first the Riemann hypothesis, then the artificial sun made by China and now about this quantum loop gravity. This truly proves that nothing is impossible…

  3. In my childhood I learned about heaven and hell which are outside our realm. Now I learn about “another branch of the space-time”. It seems that some physicists publish their visions similarly to biblical prophets. Star Trek movies had shown how people can travel faster than light. Did they show how to switch to a parallel Universe?

  4. Helpful article on singularity, space time and gravity. I especially like your adding a link to the original article.
    Following are some of my thoughts on the matter. According to current theory, small pieces of randomly moving matter in space attract each other with their individual minuscule gravitational fields and thereby eventually form increasing larger amounts of matter, eventually leading to stars and planets. The high concentrations of matter warp nearby space-time and create a gravity effect.

    The Einstein field equations EFE describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. A re-interpretation of the EFE could lead to the following alternative explanation of how matter collects to form planets and stars, and how spacetime is warped by matter. Rather than matter first collecting, and then distorting space-time and thereby creating gravity effect, I hypothesize  that discontinuous areas of SpaceTime could result in concentrated areas of gravity which then attract collections of matter. In a way, this is a reversal of the classic chicken (matter) or the egg (gravity) argument.

  5. @Donald Marks: Amazing idea! The answer to the chicken, egg question would be a link between Einstein general relativity and Standard Model

    P.S unless the existence of the question itself is already the link… 🙂

  6. @Donald Marks: [brainstorming idea] imagine that this primal energy points is pushed towards or away from each other through the ripples caused by those more dense areas of matter/energy which drives us into a conclusion what are those ripples made of? Highs Field 2.0 :). Interesting thought.

  7. Thank you for the article. This is all well beyond my ability to comment upon, but I find it absolutely fascinating nonetheless

  8. Though I’ve not gained much knowledge yet(self studying for engeenering) but I could say that there exists no universal law …All laws that we say governing nature and not actually accepted everywhere ,every law is restricted upto its own world!!!This is my thought!!!I know I’m mad and so just what I think I just made this mad comment!!!

  9. Jay Impellizzeri | December 22, 2018 at 11:48 am | Reply

    Does anti-singularity combine with non-locality (re: I think Bell) to demonstrate a multitude, perhaps observably preceding the appearance of a space-time singularity?

  10. “Reality is an illusion, however make your illusion worthwhile.”~Wayne Hicks

  11. Ikeyi Oghenekparobo | December 22, 2018 at 2:39 pm | Reply

    Great article!
    It seems there will never be a fully established universal theory or law after all; a new discovery will always be made, one that will disprove and extend a previously held one (no matter how reverential we may uphold the latter, or how great the postulator may be-Enstein, Newton,etc.) Einstein’s General Relativity predicts the existence of a singularity at the centre of a black hole, now this Loop Quantum Gravity theory disproves that; Newtonian Mechanics assumes a universal time frame, and Einstein’s theory says there’s no such a thing as that.
    One theory says something and a new, more robust one comes along that paints quite a different, more general picture.
    This is the nature of Physics, and Science in general. Knowledge grows, and previously held theories crumble in wake of new ones. The search for an ultimate theory of the universe will forever be elusive!

  12. Israel Ospina Londoño | December 22, 2018 at 6:26 pm | Reply

    Interesante artículo. Sobre todo muy importante ya que si se comprueba, sería el inicio o tal vez la continuación de la caída de elementos fundamentales de la Teoría de la Relatividad de Albert Einstein (si no fué un plagio a los físicos Poincaré, Lorentz, Heiysenberg y otros).
    Hace mucho tiempo estaba buscando un sitio como este.

  13. If one takes into account the axial Doppler shift, there is additional dimensions for time perceived by and observer of a moving object (proper time). Because there is the angle of observation in the axial Doppler shift (angle between a line from the observer to the observed and the motion). Multi-dimension time kills General relativity. For a discussion of this go to this link:

  14. If there’s no singularity then the density wont be infinite and subsequently the energy emitted by it wont be infinite too.. so by Einstein’s theory their gravitational pull would be less than that actually predicted wont it?

  15. Albert Einstein was wrong about the speed of light for which that was just his perception through a vacuum. Therefore, the speed of light is infinite in my opinion.

  16. General Theory of, not Theory of General. The theory is general, not the relativity.

  17. Math is nothing more than a linguistic metaphor, a map for describing our experiences. We must remember that the map is not the territory. Math is a linear system, and there are no strait lines in reality, just circles and spirals. Can math accurately describe these? NO!
    PI=3.141592654… :it can not be written down!
    PHI=1.618…. :it can not be written down!
    We can use math to a precision that works for describing OUR EXPERIENCES. That does not mean it is the translation of reality.
    IF people could finally find the “Universal Equation” that completely describes the universe, bringing together all the equations that they have to describe all the phenomenon in the Universe (an unrealistic expectation of “God” by my guess) they will find that the Buddha described it years ago in another language, and the Vedas before that. In math it is:
    (1=0=∞) (one=zero=infinity: we each are are nothing yet everything)
    When theoretical physicists factor in the findings of Cognitive Science they will begin to understand that.
    Or at least that is what came to me while meditating.

    • Send me more details of it

      • I read George Lakoff ([was/is?] professor of Linguistics at the University of California, Berkley): “Women, Fire, and Dangerous Things: What Categories Reveal about the Mind”; but, with Mark Johnson, “Metaphors We Live By” may better express the Cognitive Science foundation of what I am trying to convey.
        There are only a handful of “base metaphors” on which all other metaphors are based, and all language is based on metaphors. These “base” metaphors are something like “in/out,” “up/down,” etc…
        Their theory is NOT that “Math can not be a universal language based on a reality that our bodies have evolved to comprehend,” (as I remember the Gnostic teachings to be that Math is God’s language that we are held to learn, if my history holds) but rather that “we understand Math in terms of our basic Embodied Mind’s perceptions, and therefore our comprehension of systems that don’t adhere to those perceptions (quantum physics) falls apart”.
        What does it mean for light to be a wave of energy and a particle at the same time? That is the translation of the Mathematical language through our natural linguistic metaphorical system into our perceptual comprehension. That only means WE CAN NOT ACTUALLY COMPREHEND THE MATH in terms of our Embodied Mind.
        The limits to this Embodied Mind may very well be unknowable to us. Therefore we come up with equations that seem to work, but when they are all added together, they simplify to 1=0=∞
        Or something like that, if I understand their proposition.

      • In other words:
        There MAY be some aspect of the Universe that we *can*not* comprehend because it will not fit into the categories of our perceptions; therefore we can not create a mathematical equation (linguistical expression) for it, and therefore our sum-of-equations becomes 1=0=∞. However, even that statement is misleading, because “aspect” is a metaphor based on the “parts” metaphor based on the “thing” metaphor which is rooted in our handful (pun intended) of Base Metaphors of the Embodied Mind; since we can understand “things” and “parts” therefore “aspects”, we could then ultimately understand what is is I am saying we can not.
        So we are stuck in a linguistical conundrum, and Math is very rooted in those same Base Metaphors of the Embodied Mind.
        Many call that “aspect” the “spiritual dimension”; but that uses words and therefore metaphors that we can understand.
        Taoist say that the Tao that can be spoken of is no the Tao.
        Somewheres in the Christian Bible it says God has no “name” other than “God” because naming “God” limits “him” to a metaphor, which is comprehend-able to us.
        Other “religions” say “God” has so many, many names (or in Hindu there are many Gods which are all part of the greater One), again because limiting “him” to a single metaphor is misleading us in to thinking we can ultimately comprehend “him”.

      • Finally, I ask, and subtly suggest in these comments, does the Embodied Mind and its natural ability to comprehend Math yield Meditational Experiences of Oneness with the Universe combined with the understanding that ultimately we are nothing in the face of everything, yet we are that everything? 1=0=∞

  18. The speed of light is not infinite, if it was your eyes couldn’t see colors, each color is a fixed speed that your retina and brain understand.Einstein is still right.

  19. Just as Eisteins theory took us beyond Newtons understanding. New theories like this will take us beyond Einsteins. It’s an exciting time with the competing theories about time, space and other dimensions.

  20. @Lynx: I gotchu, bro

  21. My bs meter has hit the speed of infinity my attention tubes have melted and above all else the price of eggs in China has remained the same as yesterday.

  22. Einstein’e relativity is a wrong theory. There is nothing called spacetime in nature, not to mention the existence of black holes as singularities of spacetime. All the theories based on relativistic spacetime model are wrong. The fatal mistake of Einstein’s relativity is that it uses Lorentz Transformation to redefine time and space and the newly defined time is no longer the physical time we measure with physical clocks. We know the physical time shown on any physical clock is T = tf/k where t is the theoretical time, f is the frequency of the clock and k is a reference frame independent calibration constant. In Newton’s mechanics, f is a reference frame independent constant too. Therefore, we can set k = f to make the clock show the theoretical time i.e. the absolute Galilean time: T = tf/k = tf/f = t.

    But in special relativity, frequency is a reference frame dependent variable and can’t be eliminated by setting k = f, thus, T can never be relativistic time t: T = tf/k != t. Therefore, relativistic time is never the clock time i.e. the physical time. On the other hand, when a clock is observed in another inertial reference frame, t’ = γt and f’ = f/γ and T’ = t’f’/k = γt(f/γ)/k = ft/k = T, which means that clock time won’t change with the change of the inertial reference frame, Lorentz invariant and absolute. That is, a clock still measures the absolute time in special relativity. As relativistic time is not the physical time we measure with physical clocks, special relativity is wrong.

    The fact that physical time (i.e. clock time) is absolute has been clearly demonstrated by the clocks on the GPS satellites which are synchronized not only relative to the ground clocks but also relative to each other, directly denies the claim of special relativity that clocks can never be synchronized relative to more than one inertial reference frame no matter how you correct them.

  23. Daurrie Kesslyn | January 18, 2019 at 11:36 am | Reply

    Besides the instruction as cause for everything imminent in existence, a function of polarity as (residual) provisional augmentations of space, light was created with space at its boundaries. The structures and compositions of matter upon their creation are derived from the atomic and subatomic plenums, expressed as sine derivation with (timed-tined-polarity, two time grids – one next to one) polarity’s (spin to tine time) all collective arrangements of these tiny constituents (polarity’s sines to twine-time) for motions of all mechanical macroscopic facts. (particle-wave)

    CP Violation

    (Spatial spin speed or universal quantum field proxies, all approximate, proximate differential variable(s) restrained by (splitting) gravitation into the other forces thus combining energy/mass to quanta/time, vice versa, [these immeasurable atomic, subatomic collective arrangements, field forms of the immaterial, some subatomic parts are also immaterial as an anti-particle’s integuments] like the unconscious as conflux to human consciousness… in an electric-magnetic dual!)

    This Truth May Scare You! (2018-2019)
    Anonymous Official

  24. hiroji kurihara | January 20, 2019 at 6:58 pm | Reply

    Equivalence principle

    On a plain, imagine two gravity sources and fine circular waves (gravity). On every point, vector of two gravity acts as a resultant force and there is a point where the resultant force disappears. Next, gravity source is one. Huge elevator cabin is in free fall. Fortunately, this elevator is empty. So, resultant force of gravity and inertial force that acts on every point of the structure does not disappear.

    Sorry, I cannot receive E-mail. I do not have PC.

  25. hiroji kurihara | January 26, 2019 at 7:43 pm | Reply

    Equivalence Principle

    Let’s start from accelerated motion. Many substances (solids, fluids, etc) are moving in various accelerated motion. According to this motion, inertial force occurs. Imagine water of a current. Involvement between inertial force and gravity will be on resultant force only.《P.S.》Acceleration is not relative and inertial force is not fictitious. The two are corresponding qualitatively and quantitatively.

    Sorry, I cannot receive E-mail. I do not have PC.

  26. hiroji kurihara | February 9, 2019 at 6:56 pm | Reply

    Equivalence principle

    Free fall of an elevator will be (one of the) problems of resultant force (composition of forces). All will be explicable as a problem of resultant force.

    There are two pictures. In each picture, vector of two forces (f = f’) acting on a point are drawn. Direction of vectors is opposite (right and left). In one picture, forces are gravity and gravity. In the other picture, gravity and inertial force. Two pictures will not be the same (an infinite small area will be also).

    Sorry, I cannot receive E-mail. I do not have PC.

  27. Science will never be able to find out and understand many phenomena in the universe because it does not know the basis of the universe. First of all, no one knows what is matter, how and from what forms and how gravity and magnetism originate and who causes them. Besides this, science did not understand the sequence of formation and processes of the origin and disappearance of celestial bodies. Black holes are not the result of a star explosion. They are created under the influence of gravity, when in a given system, it accumulates so much mass that it represents a critical mass and critical gravity, when the matter returns to the form of the substance from which it was formed, and that substance is Aether that fills the infinite universe. Einstein’s Fatamagoras have been entangled in science, and to this day, many theories are unsurpassed and have no foothold in natural laws.

  28. Hiroji Kurihara | March 17, 2019 at 7:19 pm | Reply

    Gravitational acceleration

    Who started to say gravitational acceleration ? Is it a technical term really ? It seems to be an adjective.

    Is there a difference between an acceleration caused by an ordinal force ? If there is not a difference, a thing called gravitational acceleration will not exist.

    • Hiroji Kurihara | April 1, 2019 at 7:31 pm | Reply

      Turn your eyes to accelerated motion and inertial force. It does not matter what gravity is.

  29. Hiroji kurihara | May 2, 2019 at 8:03 pm | Reply

    Allow me to show new URL of my web site (service of geocities japan ends on Mar 2019).

  30. Equivalence principle

    Every inertial force is measurable. Every gravitational force is measurable also. Principally. In an elevator in free fall, there is no exception.

  31. An elevator in free fall

    Are the two indistinguishable? Vector of the two are opposite.

  32. Equivalence principle

    In space, there are two gravitational sources (point source). In the middle of the two, a small area is selected. This area will be a state of weightlessness (not zero gravity). Like an elevator in free fall.

  33. Gerges Francis Tawdrous | June 2, 2019 at 10:21 am | Reply

    Best Regards
    Why This Equation Is Incomplete One?
    The matter is created in motion (my hypothesis)
    That means without motion the matter will be perished –
    The motion here means the matter outer motion – as the moon motion around Earth- and I don’t mean the atoms motion inside the matter-
    The Matter is created with the space because the space is the necessary component for the matter motion-
    That means
    The matter and space are created from the same origin to be complementary to each other
    That’s why the previous Equation is incomplete one
    ETotal = EMass + ESpace
    ETotal = mc2 + ESpace
    This is The complete Equation
    Please read my paper
    Special Theory Of Relativity (Questions For Discussion)
    Gerges Francis Tawdrous +201022532292

  34. Hiroji kurihara | September 23, 2019 at 6:31 pm | Reply

    Free fall

    There is inumerable vectors of inertial forces and gravity everywhere. On an elevator cabin, why they are making a big fuss ?

  35. Difference of motion

    Differene of inertial motion and accelerated motion will be difference of motion relative to aether frame. And accelerated motion and inertial force are the front and back of a fact. Inertial force is not a fictitious force.

  36. Hiroji kurihara | September 24, 2019 at 1:11 pm | Reply

    Horizontal Doppler effect

    On a plane, pararell lines are drawn. On each line, light sources (frequency is the same ) are moving in the opposite direction. Imagine light sources form japanese letter エ. Phenomenon horizontal Doppler effect will not be.

  37. New equivalence principle ?

    A passenger car is accelerating (at a, to the right). A body is hung from the roof by a string. Can the string distinguish mg caused by acceleration and by gravity ? No, it is a joke. But a picture of an elevator seems to be a joke also.

  38. Accelerated motion
    Accelerated motion will be the motion relative to aether frame. Vector causes the same vector of inertial force. Gravity has no connection.

    From every inertial frame, accelerated motion is possible to know qualitatively and quantitatively.

  39. Hiroji kurihara | October 2, 2019 at 9:22 pm | Reply

    A site on anti relativity
    A web site written by member volunteers of Japan science council is now being published (in Japanese). URL is

  40. Equivalence principle
    Two forces the same vector in strength are acting on a particle from the opposite. The two are inertial force, tension and gravity. Different combinations are three. Forget the equivalence principle.

  41. Equivalence principle
    From the roof of an elevator cabin, a body is hung by a string. The elevator begins acceleration upward. Can the string distinguish between gravity and inertial force ?

  42. Equivalence principle
    An elevator in free fall is explained fully by Newton. There is no room for Einstein.

  43. Gravitational mass and inertial mass
    A point mass is falling in free fall. According to the law of action and reaction, gravity and inertial force are equal. And g and a, as acceleration are equal also (direction is opposite). So, two mass are equal (mass is mass !?).

  44. Acceleration and non acceleration
    On a plane (no friction), there is a body. Difference between the two above will be evident. It is enough to keep an eye on inertial force.

  45. Inertial force
    Inertial force is depending on m. So, it is not fictitious.

  46. Acceleration and non acceleration
    On a plane, there is a body. Different between the two above will be evident. It is enough to keep an eye on inertial force.

  47. Acceleration
    True identity of acceleration must be shown by inertial force or geometrical expression of motion starting from an inertial frame. Though it is a great formula ; F = ma, acceleration will not be connected directly to external force.

  48. Inertial force

    On a slope (no friction), a body is sliding down. Action is gravity mg. Then, how about the reaction ? It is resolved to two vectors. Inertial force is not fictitious.

  49. Equivalence principle is nonsense (I say again)

    An elevator in free fall is explained fully by Newton. No different explanation is possible. And it is the same even if limited to the infinite small area.

  50. Inertial force is not fictitious

    On a plane, there are two bodies. One is at a standstill, the other is accelerating. Acceleration (a) and inertial force (ma) both are not fictitious.

    There are two disks. One is not rotating, the other is rotating. Acceleration and inertial force both are not fictitious.

  51. Acceleration

    From nothing, a seems not to emerge. By acceleration of body relative to aether, am will emerge. Qualitatively and quantitatively.

  52. Acceleration (I say again)

    On a plane, a straight line is drawn. On this line, two bodies are receding. One is at a standstill, the other is accelerated uniformly. On the one, inertial force is emerging but not on the other. All is shown by a and ma.

    But what distinguishes acceleration and nonacceleration ? In above picture, uniform isotropic aether will be hidden. This picture is not picture of geometry.

  53. Space is rest frame

    Into space, let us draw plural vectors of acceleration a. Space will be rest frame.

  54. Elf fires

    Are there still berievers of relativity? Elf fires. It is not a thing of this world.

  55. Equivalence principle (I say again)

    Vector of inertial force is shown by an arrow. Vector of gravity cannot be shown by an arrow generally. The two are different generally as pHysics facts.

  56. Accelerated frame and non-accelerated frame

    There are plural accelerated frames and plural non-accelerated frames. The two will not be relative.

  57. Aether

    Speed of light relative to mediums (water or air) is constant. Speed of light relative to aether (physical substance) is constant also. Aberrations show this.

  58. About inertial force (I say again)

    On a plane, there are two passenger cars. One is accelerating and the other is at a standstill. Difference of the motion of the two is not relative but absolute.

    On a plane, a passenger car is accelerating. On the floor (no friction), a body is put. This body is not accelerated (to everyone). In physics of 20th century, nonsenses overflow.

  59. Sagnac effect

    Let’s try to explain Sagnac effect by the emission theory. There is a picture of light pathes (a light source and two mirrors form equilateral triangle). On this triangle, there are three emission points,(different inertial frames). It will be a cause of this effect.

  60. Equivalence principle

    Difference between acceleration and nonacceleration seems to be more basic. If so, equivalence principle is invalid.

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