*Ta-Pei Cheng*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573639
- eISBN:
- 9780191722448
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573639.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Black hole is an object so compact that it is inside its event horizon: a one-way surface through which particle and light can only traverse inward, and an exterior observer cannot receive any signal ...
More

Black hole is an object so compact that it is inside its event horizon: a one-way surface through which particle and light can only traverse inward, and an exterior observer cannot receive any signal sent from inside. The Schwarzschild geometry is viewed in the Eddington-Finkelstein coordinates as well as in the Kruskal coordinates. Besides a black hole, the GR field equation also allows the solution of a white hole and a wormhole. The gravitational energy released when a particle falls into a tightly bound orbit around a black hole can be enormous. The physical reality of, and observational evidence for, black holes are briefly discussed. Quantum fluctuation around the event horizon brings about the Hawking radiation. This and the Penrose process in a rotating (Kerr) black hole comes about because of the possibility of negative energy particles falling into a black hole.Less

Black hole is an object so compact that it is inside its event horizon: a one-way surface through which particle and light can only traverse inward, and an exterior observer cannot receive any signal sent from inside. The Schwarzschild geometry is viewed in the Eddington-Finkelstein coordinates as well as in the Kruskal coordinates. Besides a black hole, the GR field equation also allows the solution of a white hole and a wormhole. The gravitational energy released when a particle falls into a tightly bound orbit around a black hole can be enormous. The physical reality of, and observational evidence for, black holes are briefly discussed. Quantum fluctuation around the event horizon brings about the Hawking radiation. This and the Penrose process in a rotating (Kerr) black hole comes about because of the possibility of negative energy particles falling into a black hole.

*Steven Carlip*

- Published in print:
- 2019
- Published Online:
- March 2019
- ISBN:
- 9780198822158
- eISBN:
- 9780191861215
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822158.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Chapter 3 used the Schwarzschild metric to obtain predictions for the Solar System. In this chapter, that metric is derived as the unique static, spherically symmetric solution of the vacuum Einstein ...
More

Chapter 3 used the Schwarzschild metric to obtain predictions for the Solar System. In this chapter, that metric is derived as the unique static, spherically symmetric solution of the vacuum Einstein field equations. For the Solar System, this vacuum solution must be joined to an “interior solution” describing the interior of the Sun. Such solutions are discussed briefly. If, on the other hand, one assumes “vacuum all the way down,” the solution describes a black hole. The chapter analyzes the geometry and physics of the nonrotating black hole: the event horizon, the Kruskal-Szekeres extension, the horizon as a trapped surface and as a Killing horizon. Penrose diagrams are introduced, and a short discussion is given of the four laws of black hole mechanics.Less

Chapter 3 used the Schwarzschild metric to obtain predictions for the Solar System. In this chapter, that metric is derived as the unique static, spherically symmetric solution of the vacuum Einstein field equations. For the Solar System, this vacuum solution must be joined to an “interior solution” describing the interior of the Sun. Such solutions are discussed briefly. If, on the other hand, one assumes “vacuum all the way down,” the solution describes a black hole. The chapter analyzes the geometry and physics of the nonrotating black hole: the event horizon, the Kruskal-Szekeres extension, the horizon as a trapped surface and as a Killing horizon. Penrose diagrams are introduced, and a short discussion is given of the four laws of black hole mechanics.

*George Jaroszkiewicz*

- Published in print:
- 2016
- Published Online:
- January 2016
- ISBN:
- 9780198718062
- eISBN:
- 9780191787553
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198718062.003.0019
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the transition from special relativistic (Minkowski) spacetime to general relativistic spacetimes. It reviews the concept of timelike, spacelike, and null (or lightlike) vector ...
More

This chapter discusses the transition from special relativistic (Minkowski) spacetime to general relativistic spacetimes. It reviews the concept of timelike, spacelike, and null (or lightlike) vector fields, as these are fundamental to the physics of general relativity. In particular, they help us define the frame fields that are the local general relativistic versions of the conventional Minkowski spacetime Cartesian coordinate frames that are used to discuss real experiments. The famous Schwarzschild (black hole) solution for a point mass source is explored, with an analysis of the light-cone structure relevant to infalling observers. Gravitational time dilation, white holes, and spinning disc frames are reviewed.Less

This chapter discusses the transition from special relativistic (Minkowski) spacetime to general relativistic spacetimes. It reviews the concept of timelike, spacelike, and null (or lightlike) vector fields, as these are fundamental to the physics of general relativity. In particular, they help us define the frame fields that are the local general relativistic versions of the conventional Minkowski spacetime Cartesian coordinate frames that are used to discuss real experiments. The famous Schwarzschild (black hole) solution for a point mass source is explored, with an analysis of the light-cone structure relevant to infalling observers. Gravitational time dilation, white holes, and spinning disc frames are reviewed.

*Piotr T. Chruściel*

- Published in print:
- 2020
- Published Online:
- December 2020
- ISBN:
- 9780198855415
- eISBN:
- 9780191889233
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198855415.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

In this chapter we present a systematic approach to extensions of spacetimes, as needed to construct black-hole spacetimes. On the way we introduce the conformal diagrams, which are a useful tool for ...
More

In this chapter we present a systematic approach to extensions of spacetimes, as needed to construct black-hole spacetimes. On the way we introduce the conformal diagrams, which are a useful tool for visualizing the geometry of the extensions. We focus on extensions of metrics containing a two-by-two stationary Lorentzian block.We discuss causality for such metrics in Section 6.1; the possible building blocs are described in Section 6.2; these building blocs are put together in Section 6.3. The general rules governing the construction are explained in Section 6.4, with the causal aspects of the construction highlighted in the short Section 6.5. The method is applied to those Birmingham metrics which have not been analysed previously in Section 6.6.Less

In this chapter we present a systematic approach to extensions of spacetimes, as needed to construct black-hole spacetimes. On the way we introduce the conformal diagrams, which are a useful tool for visualizing the geometry of the extensions. We focus on extensions of metrics containing a two-by-two stationary Lorentzian block.We discuss causality for such metrics in Section 6.1; the possible building blocs are described in Section 6.2; these building blocs are put together in Section 6.3. The general rules governing the construction are explained in Section 6.4, with the causal aspects of the construction highlighted in the short Section 6.5. The method is applied to those Birmingham metrics which have not been analysed previously in Section 6.6.