Invariance properties are related with underlying symmetries of a theory. The most sacred of them is the conservation of energy on which thermodynamics is based (for example supplied heat energy to a system is the sum of change of internal energy and external work done). Conservation of energy is related with the time-translation invariance through Noether's theorem. In GTR, which is fundamentally a "geometric theory" of gravity, a non-zero energy-momentum four vector (of a particle or an object) can induce a curvature of space time. In other words space-time manifold is distorted near the source breaking time translation invariance of the theory locally and hence breaking conservation of energy locally. Sufficiently far away for the source, however, one can restore the notion of asymptotic flatness, where again conservation of energy is valid, which again restores thermodynamic laws.

General relativity is a relativistic theory of gravitation and can be applied to even one body or two body problems in which initial data is known completely so that the states at any future time can be obtained by solving differential equations. Thermodynamics is applicablue when the number of degrees of freedom is very large. There is no known incompatibility between the two theories. It is just that GR equations are very difficult to solve and hence dealing with a large number of gravitating bodies is hard in GR.

Dear Biswajoy, and Patrick,

Are you aware of the thermodynamical fact that, one intensive (extensive) variable can only be defined in terms of another intensive (extensive) variable only? If your answer is Yes, then see how Temperature and Entropy has been defined in GTR ...Pdf file is attached to this post..

Also, Conservation of energy can not be broken either locally or non-locally in space and time.... GTR has very serious flaw...

Gokaran, all I am saying is that as long as you are not near a very massive object like a black hole, your conventional wisdom is unhurt and safe. Near a super massive object if you are close enough to it's event horizon, Physics changes considerably due to local changes in space time geometry. For example the notion of entropy has to be redefined. See also works on Bekenstein-Hawking entropy.

Dear Biswajoy,

Conservation of energy, conservation of momentum , conservation of angular momentum principle are applied in every-system any-day anytime... Also, definition of entropy should not be changed... Every operational -non-operational device ], everything which exist in nature follows the second law of thermodynamics.... Entropy is the consequence of the second law of thermodynamics.... Notion of entropy can not be changed... Notion of temperature can not be changed... I hope you have read Arthur Edington views on the second law of thermodynamics... Read it again... First you need to explain that whether is it possible to define one intensive variable in term of extensive variable? This is fundamental rule of thermodynamics... This is as important as the matching of dimensional analysis of left hand with right hand side in any physical equation ..

And how do you know that Hawking black hole radiation theory and entropy are correct? You can play with mathematical equations, but consequence of that equations are not necessary depicting the any reality of nature... You might have heard one of the Great scientist Pauli famous quote " Its not even WRONG"

Of-course as you have rightly said that we do not like to change fundamental principles such as the conservation of energy etc. They are so successful otherwise. However when situation is drastically different, then, I suppose one should not take a very rigid outlook. In such a situation our physical intuitive approach has to be replaced by some new mathematical formulation. In the history of science such turning points have appeared in several occasions. You could say "old order changeth yielding place to the new" --Tennyson.

Old order can only be changed if they have certain flaw in the reasoning...I don't think there is any flaw in the conservation of energy, conservation of linear momentum, conservation of angular momentum and in the second law of thermodynamics...Most of the people who have challenged these rule have almost negligible experienced with quantum mechanical system, where these rules has been tested multiple occasions..

Gokaran, it is not the purpose of general relativity (GR) to define temperature and entropy. These are defined by statistical mechanics/thermodynamics, since these pertain to very large no. of degrees of freedom and our ignorance of precise values of phase space variables for systems containing large no. of particles. GR and gravitational physics use the standard definitions in systems of their interest. For example, it then turns out that a gravitationally bound state comprising of many stars has negative specific heat when one uses standard thermodynamics.

So, I completely disagree with your statement that GR defines intensive thermodynamic quantities on its own. It is like saying Maxwell's electrodynamics (ED) defines temperature and entropy. GR and ED are simply relativistic theories of gravity and electromagnetism, respectively.

Dear Patrick,

I hope you do understand, that every existence entity in the universe has made form elements (material).... I hope you do understand the definition of specific heat.. "The amount of energy required to raise the system temperature by one Kelvin" .. If you accept this standard definition, then it will be IMPOSSIBLE that any system have negative specific heat...

If you lookup the Hawking entropy and Temperature, then you will notice yourself that they are violating every rule of the standard thermodynamics... Please see the attached slides..

Please read Lynden-Bell's article on this https://arxiv.org/pdf/cond-mat/9812172.pdf

And Hawking radiation does not fall in the GR category. It belongs to the subject of quantum field theory in the black hole background.

Dear Patrick,

According to GTR, black holes does exist. Hawking only uses GTR reasoning and proved that they emit radiation. So, if you discard Hawking radiation, then indirectly you are discarding Blackhole and GTR as well..

This conjecture has some interest. But it depends on the definition of a Gravitation Wave (GW). When a mass moves, the effect on other mass changes. But is a ripple or a wave. (definition)A ripple is when the potential effect changes to 1/r and remains 1/r as long as r remains constant. A wave obeys the wave equation. So, the waving medium has inertia. If spacetime has inertia then it should show wave characteristics. The statement that it does not show (not having been observed ?) reflection, diffraction, etc. is more of a situation that nobody has looked correctly or that the propagating gravity changes are really ripples and not waves. So, energy is transferred by the effect on masses and not by the transmittal. This is thermal energy. So, problem does not exist.

Gokaran, as far as Hawking Radiation calculation is concerned, key concepts are the notion of particle in the vicinity of a black hole and validity of quantum field theory in curved space-time. So, if these notions undergo modifications, there may not be any Hawking radiation (HR). On the other hand GR has been tested many times and existence of classical black holes have been corroborated by astronomers. Hence GR will not get dented, even if HR is falsified.

Albert Einstein, creator of GTR, eulogizes thermodynamics:

"Classical thermodynamics … is the only physical theory of universal content which I am convinced … will never be overthrown."

Not a student of GTR, I however do have faith in the universality of the 2nd law. This law is among the fundamentals forming basis of whatever course one picks on classical thermodynamics.

@ Gokaran Shukla

my dear Gokaran Shukla , it is good question from you....the data you provided (only on gravitational waves) is insufficient to claim farewell of GTR is very very near...we need to provide better support to farewell GR...we are still in confusion regarding gravitational waves and not that much handy like EM waves...

The so-called "entropy " doesn't exist at all.

During the process of deriving the so-called entropy, in fact, ΔQ/T can not be turned into dQ/T. That is, the so-called "entropy " doesn't exist at all.

The so-called entropy was such a concept that was derived by mistake in history.

It is well known that calculus has a definition,

any theory should follow the same principle of calculus; thermodynamics, of course, is no exception, for there's no other calculus at all, this is common sense.

Based on the definition of calculus, we know:

to the definite integral ∫T f(T)dQ, only when Q=F(T), ∫T f(T)dQ=∫T f(T)dF(T) is meaningful.

As long as Q is not a single-valued function of T, namely, Q=F( T, X, …), then,

∫T f(T)dQ=∫T f(T)dF(T, X, …) is meaningless.

1) Now, on the one hand, we all know that Q is not a single-valued function of T, this alone is enough to determine that the definite integral ∫T f(T)dQ=∫T 1/TdQ is meaningless.

2) On the other hand, In fact, Q=f(P, V, T), then

∫T 1/TdQ = ∫T 1/Tdf(T, V, P)= ∫T dF(T, V, P) is certainly meaningless. ( in ∫T , T is subscript ).

We know that dQ/T is used for the definite integral ∫T 1/TdQ, while ∫T 1/TdQ is meaningless, so, ΔQ/T can not be turned into dQ/T at all.

that is, the so-called "entropy " doesn't exist at all.

Gokaran's question above is very deep indeed.

The starting point of thermodynamic logic is: 1) opposing perpetual motion. 2) The irreversibility of dynamics. Let's look at how to get Carnot efficiency = 1-T1/T2.

1.1 There are many kinds of type 2 perpetual motors, each of which is a natural phenomenon.

A) Machine A: against the irreversibility of thermodynamics (diffusion, heat conduction, friction, etc) - dynamics;

B) Machine B: Utilizing the Difference of Carnot Efficiency (Reversible Thermodynamics) - Thermodynamics

1.2 A and B belong to different disciplines. There is a parallel relationship between them and there is no logical mutual inevitability.

1.3. Logic of the Second Law of Thermodynamics:

Experience induction, deny that A machine==> B machine can not be manufactured==> All material Kano efficiency: 1-T1/T2.

1.4 The logic of the second law of thermodynamics violates the physical logic that A and B cannot be inferred from each other.

1.5 The second law of thermodynamics elevates the "irreversibility", which is in fact only a kinetic experience.

📷 Detailed discussion can be found in the following figure.