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Schwarzschild coordinates

About: Schwarzschild coordinates is a research topic. Over the lifetime, 344 publications have been published within this topic receiving 7151 citations.


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TL;DR: In this article, the authors considered the problem of a small particle falling in a Schwarzschild background ("black hole") and examined its spectrum in the high-frequency limit, in terms of the traceless transverse tensor harmonics called electric and magnetic by Mathews.
Abstract: We are concerned with the pulse of gravitational radiation given off when a star falls into a "black hole" near the center of our galaxy. We look at the problem of a small particle falling in a Schwarzschild background ("black hole") and examine its spectrum in the high-frequency limit. In formulating the problem it is essential to pose the correct boundary condition: gravitational radiation not only escaping to infinity but also disappearing down the hole. We have examined the problem in the approximation of linear perturbations from a Schwarzschild background geometry, utilizing the decomposition into the tensor spherical harmonics given by Regge and Wheeler (1957) and by Mathews (1962). The falling particle contributes a $\ensuremath{\delta}$-function source term (geodesic motion in the background Schwarzschild geometry) which is also decomposed into tensor harmonics, each of which "drives" the corresponding perturbation harmonic. The power spectrum radiated in infinity is given in the high-frequency approximation in terms of the traceless transverse tensor harmonics called "electric" and "magnetic" by Mathews.

708 citations

Journal ArticleDOI
TL;DR: The spherically symmetric vacuum stress energy tensor with one assumption concerning its specific form generates the exact analytic solution of the Einstein equations which for larger coincides with the Schwarzschild solution, for smallr behaves like the de Sitter solution as mentioned in this paper.
Abstract: The spherically symmetric vacuum stress-energy tensor with one assumption concerning its specific form generates the exact analytic solution of the Einstein equations which for larger coincides with the Schwarzschild solution, for smallr behaves like the de Sitter solution and describes a spherically symmetric black hole singularity free everywhere.

550 citations

Journal ArticleDOI
TL;DR: In this paper, a general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed, which can handle more general situations such as: (i) Spacetimes which are not asymptotically flat (such as the de Sitter spacetime), and (ii) Spaces with multiple horizons having different temperatures, such as the Schwarzschild-de Sitter, Reissner-Nordstrom horizons, providing a consistent interpretation for temperature, entropy and energy.
Abstract: A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black-hole spacetimes and can handle more general situations such as: (i) spacetimes which are not asymptotically flat (such as the de Sitter spacetime) and (ii) spacetimes with multiple horizons having different temperatures (such as the Schwarzschild–de Sitter spacetime) and provide a consistent interpretation for temperature, entropy and energy. I show that it is possible to write Einstein's equations for a spherically symmetric spacetime in the form T dS − dE = P dV near any horizon of radius a with S equal; 1/4(4πa2), |E| = (a/2) and the temperature T determined from the surface gravity at the horizon. The pressure P is provided by the source of Einstein's equations and dV is the change in the volume when the horizon is displaced infinitesimally. The same results can be obtained by evaluating the quantum mechanical partition function without using Einstein's equations or the WKB approximation for the action. Both the classical and quantum analyses provide a simple and consistent interpretation of entropy and energy for de Sitter spacetime as well as for (1 + 2) dimensional gravity. For the Rindler spacetime the entropy per unit transverse area turns out to be 1/4 while the energy is zero. The approach also shows that the de Sitter horizon—like the Schwarzschild horizon—is effectively one dimensional as far as the flow of information is concerned, while the Schwarzschild–de Sitter, Reissner–Nordstrom horizons are not. The implications for spacetimes with multiple horizons are discussed.

549 citations

Journal ArticleDOI
TL;DR: In this article, a spherically symmetric solution of the Einstein equations is presented that coincides with the exterior Schwarzschild solution, but where the Schwarzschild "sphere" becomes a point singularity.
Abstract: A spherically symmetric solution of the Einstein equations is presented that coincides with the exterior ($\mathcal{r}g2m$) Schwarzschild solution, but where the Schwarzschild "sphere" becomes a point singularity. The possible relevance of this solution to the question of gravitational collapse is discussed.

436 citations

Journal ArticleDOI
TL;DR: In this paper, the influence of a plasma on the shadow of a supermassive black hole was analyzed. But the authors restricted their analysis to spherically symmetric and static situations, where the shadow is circular and the plasma is assumed to be nonmagnetized and pressureless.
Abstract: We analytically calculate the influence of a plasma on the shadow of a black hole (or of another compact object). We restrict to spherically symmetric and static situations, where the shadow is circular. The plasma is assumed to be nonmagnetized and pressureless. We derive the general formulas for a spherically symmetric plasma density on an unspecified spherically symmetric and static spacetime. Our main result is an analytical formula for the angular size of the shadow. As a plasma is a dispersive medium, the radius of the shadow depends on the photon frequency. The effect of the plasma is significant only in the radio regime. The formalism applies not only to black holes but also, e.g., to wormholes. As examples for the underlying spacetime model, we consider the Schwarzschild spacetime and the Ellis wormhole. In particular, we treat the case that the plasma is in radial free fall from infinity onto a Schwarzschild black hole. We find that for an observer far away from a Schwarzschild black hole, the plasma has a decreasing effect on the size of the shadow. The perspectives of actually observing the influence of a plasma on the shadows of supermassive black holes are discussed.

243 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202112
20202
20197
20183
201711
201612