Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime: Part III—Realization of Exact Solutions
This is the Part III paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework for the gauge-invariant perturbation theory and the proposal for gauge-invariant treatments of <inline-formula><math x...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Universe |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-1997/11/2/52 |
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| Summary: | This is the Part III paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework for the gauge-invariant perturbation theory and the proposal for gauge-invariant treatments of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></semantics></math></inline-formula> mode perturbations on the Schwarzschild background spacetime in the Part I paper, we examine the problem of whether the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></semantics></math></inline-formula> even-mode solutions derived in the Part II paper are physically reasonable. We consider the linearized versions of the Lemaître–Tolman–Bondi solution and the non-rotating C-metric. As a result, we show that our derived even-mode solutions to the linearized Einstein equations realize these two linearized solutions. This supports the conclusion that our derived solutions are physically reasonable, which implies that our proposal for gauge-invariant treatments of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></semantics></math></inline-formula> mode perturbations is also physically reasonable. We also briefly summarize the conclusions of our series of papers. |
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| ISSN: | 2218-1997 |