--- title: "Gravitational Wave Emission and Mass Extraction from a Perturbed Schwarzschild Black Hole • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb525" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Gravitational%2BWave%2BEmission%2Band%2BMass%2BExtraction%2Bfrom%2Ba%2BPerturbed%2BSchwarzschild%2BBlack%2BHole%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TS4gQy4gTGltYTsgSXZhbm8gRGFtacOjbyBTb2FyZXM%2Cdetalhe_1997%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI1MjUi%2Cs_USsX71bJgSqWBcZe.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Gravitational Wave Emission and Mass Extraction from a Perturbed Schwarzschild Black Hole • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Gravitational%2BWave%2BEmission%2Band%2BMass%2BExtraction%2Bfrom%2Ba%2BPerturbed%2BSchwarzschild%2BBlack%2BHole%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TS4gQy4gTGltYTsgSXZhbm8gRGFtacOjbyBTb2FyZXM%2Cdetalhe_1997%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI1MjUi%2Cs_USsX71bJgSqWBcZe.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Gravitational Wave Emission and Mass Extraction from a Perturbed Schwarzschild Black Hole** **M. C. Lima; Ivano Damião Soares** 1997 [**Download PDF **0.2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb525/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Gravitational%20Wave%20Emission%20and%20Mass%20Extraction%20from%20a%20Perturbed%20Schwarzschild%20Black%20Hole) ## **Publication details**
Authors
M. C. Lima; Ivano Damião Soares
Type
Physics Note
Status
Published
Publication date
1997
Description
A relativistic model for the emission of gravitational waves from an initially unperturbed Schwarzschild black hole, or spherical collapsing configuration, is completely integrated. The model consists basically of gravitational perturbations of the Robinson-Trautman type on the Schwarzschild spacetime. In our scheme of perturbation, gravitational waves may extract mass from the collapsing configuration, and the amount of mass extracted depends on the particular gravitational wave l-poles emitted <math>(l\geq 2)\,\!</math>. The formulation allows us to define a mass emissity function <math>\left.e_l=\displaystyle{\displaystyle{\frac{3b_0}{2}}}\right/ \left[\displaystyle{\frac{l(l+1)}{2}} \left(\displaystyle{\frac{l(l+1)}{2}}-1\right)\right]\,\!</math>, which measures the ratio of mass taken out from the source by a <math>l\,\!</math>-pole <math>(b_0\,\!</math> is a small positive parameter, of the order of the perturbations, characteristic of the mechanism of mass emission in a Schwarzschild background spacetime). The quadrupole emission mode is the dominant mechanism in extracting mass from the configuration. Robinson-Trautmann perturbations also include another mode of emission of mass, which we denote shell emission mode: in the equatorial plane of the configuration, a timelike (1+2) shell of matter may be present, whose stress-energy tensor is modelled by neutrinos and strings emitted radially on the shell; no gravitational waves are present in this model. The invariant characterization of gravitational wave perturbations and of the gravitational wave zone is made through the analysis of the structure of the curvature tensor and the use of the Peeling Theorem. The time behaviour of a l-pole gravitational wave has the form exp <math> [-(u/3M)l(l + 1)/2 (l(l+1)/2-1)]\,\!</math> where M is the initial mass of the collapsing configuration and u may be interpreted asymptotically as the retarded time. It follows that, for a Galilean observer at infinity, the horizon of the final black hole configuration takes an infinite time to form.
Year
1997
Number
CBPF-NF-046/97
Linked to a thesis
No
Linked to a grant
No
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