scholarly journals Is there a general area theorem for black holes?

1998 ◽  
Vol 39 (12) ◽  
pp. 6603-6606 ◽  
Author(s):  
Domenico Giulini
Keyword(s):  
Black Holes ◽  
General Area ◽  
Area Theorem

scholarly journals A general area theorem for the same-different paradigm

2008 ◽  
Vol 70 (5) ◽  
pp. 761-764 ◽  
Author(s):  
C. MICHEYL ◽  
H. DAI
Keyword(s):  
General Area ◽  
Area Theorem

scholarly journals HORIZON MASS THEOREM

2005 ◽  
Vol 14 (12) ◽  
pp. 2219-2225 ◽  
Author(s):  
YUAN K. HA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uniqueness Theorem ◽  
Hawking Radiation ◽  
General Theorem ◽  
Positive Energy ◽  
Singularity Theorem ◽  
Area Theorem ◽  
Classical Black Holes ◽  
The Uniqueness Theorem

A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes, neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed at infinity. Previous theorems on black holes are: (i) the singularity theorem, (ii) the area theorem, (iii) the uniqueness theorem, (iv) the positive energy theorem. The horizon mass theorem is possibly the last general theorem for classical black holes. It is crucial for understanding Hawking radiation and for investigating processes occurring near the horizon.

scholarly journals Study of black hole as dissipative structure using negentropy

2016 ◽  
Vol 94 (10) ◽  
pp. 960-966
Author(s):  
Shripad P. Mahulikar ◽  
Pallavi Rastogi
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Theoretical Investigation ◽  
Infinite Number ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Area Theorem ◽  
Entropy Increase ◽  
The Universe

The area of the event horizon of a black hole (Aeh) is so far linked only with its entropy (SBH). In this theoretical investigation, it is shown that relating Aeh only to SBH is inadequate, because Aeh is linked to the black hole’s negentropy, which encompasses its entropy. Increasing Aeh of black holes that grow now follows from the negentropy theorem (NET) and also from the well-known area theorem. The decreasing Aeh of black holes that decay follows from the converse to NET and is not a violation of the area theorem. The corollary to NET is proved for the case when two dissipative structures merge, which is the basis for the coalescence of black holes. The converse of corollary to NET explains negentropy loss due to splitting of a dissipative structure. When applied to black hole explosion (i.e., splitting into an infinite number of parts), converse of corollary to NET reduces to converse of NET. The entropy/energy ratio of the exported Hawking radiance from black holes contributes to the entropy increase of the universe. These aspects justify the consideration of black holes as thermodynamic dissipative structures.

scholarly journals HEAD-ON COLLISION AND MERGING ENTROPY OF BLACK HOLES: RECONSIDERATION OF HAWKING'S INEQUALITY

2013 ◽  
Vol 22 (07) ◽  
pp. 1350050 ◽  
Author(s):  
MASARU SIINO
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Upper Bound ◽  
Gravitational Radiation ◽  
High Energy ◽  
Black Hole Thermodynamics ◽  
Black Hole Horizon ◽  
Energy Ratio ◽  
Area Theorem ◽  
Numerical Investigations

We evaluate the amount of energy that can be converted into gravitational radiation in head-on collision of black holes. We estimate it by the area theorem of black hole horizon incorporating merging entropy of colliding black holes from a viewpoint of black hole thermodynamics. Then we obtain an upper bound of energy ratio of the gravitational radiation which is smaller than the upper bound originally derived by Hawking. The fact that this estimation is not inconsistent with the results of both numerical investigations in low- and high-energy head-on collision implies that thermodynamics of coalescing black holes requires the contribution of the merging entropy.

Some applications

2020 ◽  
pp. 85-114
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Wave Equation ◽  
Black Hole Thermodynamics ◽  
Splitting Theorem ◽  
Short Discussion ◽  
Area Theorem ◽  
Black Hole Spacetimes ◽  
Singularity Theorems ◽  
Incompleteness Theorems

The aim of this chapter is to present key applications of causality theory, as relevant to black-hole spacetimes. For this we need to introduce the concept of conformal completions, which is done in Section 3.1. We continue, in Section 3.2, with a review of the null splitting theorem of Galloway. Section 3.3 contains complete proofs of a few versions of the topological censorship theorems, which are otherwise scattered across the literature, and which play a basic role in understanding the topology of black holes. In Section 3.4 we review some key incompleteness theorems, also known under the name of singularity theorems. Section 3.5 is devoted to the presentation of a few versions of the area theorem, which is a cornerstones of ‘black-hole thermodynamics’. We close this chapter with a short discussion of the role played by causality theory when studying the wave equation.

Elements of causality

2020 ◽  
pp. 21-84
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Energy Conditions ◽  
Lorentzian Manifolds ◽  
Area Theorem ◽  
Causal Relations ◽  
Singularity Theorems ◽  
The Subject ◽  
Incompleteness Theorems ◽  
Uniqueness Theory

A standard part of studies of black holes, and in fact of mathematical general relativity, is causality theory, which is the study of causal relations on Lorentzian manifolds. An essential issue here is understanding the influence of energy conditions on the causality relations. The highlights of such studies include the incompleteness theorems, known also as singularity theorems, of Penrose, Hawking and Geroch, the area theorem of Hawking, and the topology theorems of Hawking and others. The aim of this chapter is to provide an introduction to the subject, with a complete exposition of those topics which are needed for the global treatment of the uniqueness theory of black holes. In particular we provide a coherent introduction to causality theory for metrics which are twice differentiable.

THOUGHTS ON THE AREA THEOREM

2009 ◽  
Vol 24 (16n17) ◽  
pp. 3111-3135 ◽  
Author(s):  
MU-IN PARK
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Three Dimensional ◽  
Kerr Black Hole ◽  
Second Law Of Thermodynamics ◽  
Positive Energy ◽  
Btz Black Hole ◽  
Area Theorem ◽  
Four Dimensions ◽  
Higher Derivative

Hawking's area theorem can be understood from a quasistationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual Banados–Teitelboim–Zanelli (BTZ) black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon "can decrease," rather than increase, with the quasistationary process. However, I find that the area for the outer horizon "never decrease" such as the usual area theorem still works in our examples, though this is quite nontrivial in general. I also find that the recently proposed new entropy formulae for the above mentioned, recently discovered black holes satisfy the second law of thermodynamics.

Black hole thermodynamics

2021 ◽  
pp. 301-316
Author(s):  
Andrew M. Steane
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Black Hole Thermodynamics ◽  
Unruh Effect ◽  
Area Theorem ◽  
Hawking Effect ◽  
Precise Calculation ◽  
Radiation Entropy ◽  
Penrose Process

The chapter presents the Penrose process, Hawking radiation, entropy and the laws of black hole thermodynamics. The Penrose process is derived and the area theorem is stated. A heuristic argument for the Hawking effect is given, emphasising a correct grasp of the concepts and the nature of the result. The Hawking effect and the Unruh effect are further discussed and linked together in a precise calculation. Evaporation of black holes is described. The information paradox is presented.

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