# Time-asymmetric initial data for black holes and black-hole collisions

## Abstract

As a first step in constructing initial data for dynamic black holes and general black-hole collisions, we study nonsingular vacuum Cauchy hypersurfaces with two isometric asymptotically flat ends connected by an Einstein-Rosen-type bridge. These hypersurfaces are assumed to be conformally flat and maximally embedded in space-time but are neither spherically symmetric nor time symmetric. Three of the four constraints are solved explicitly for suitable extrinsic curvature tensors that possess linear momentum and/or intrinsic angular momentum. The complete initial data are shown to transform invariantly, modulo the sign of the extrinsic curvature tensor, under inversion through a minimal two-surface that represents the ''throat'' of the geometry. These and other properties show that the data represent a particular epoch in the history of a dynamic black hole. We describe the relation of our data to that of the Schwarzschild and Kerr black holes. Finally, we discuss the generalization to encounters of two or more black holes.

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27514

- OSTI Identifier:
- 5392738

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev., D; (United States)

- Additional Journal Information:
- Journal Volume: 21:8

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BLACK HOLES; COLLISIONS; SPACE-TIME; VACUUM STATES; ANGULAR MOMENTUM; BOUNDARY-VALUE PROBLEMS; EINSTEIN FIELD EQUATIONS; GENERAL RELATIVITY THEORY; GRAVITATIONAL FIELDS; KERR METRIC; PERTURBATION THEORY; SCHWARZSCHILD RADIUS; TENSOR FORCES; TWO-BODY PROBLEM; EQUATIONS; FIELD EQUATIONS; FIELD THEORIES; MANY-BODY PROBLEM; METRICS; 640102* - Astrophysics & Cosmology- Stars & Quasi-Stellar, Radio & X-Ray Sources; 657003 - Theoretical & Mathematical Physics- Relativity & Gravitation

### Citation Formats

```
Bowen, J.M., and York, J.W. Jr..
```*Time-asymmetric initial data for black holes and black-hole collisions*. United States: N. p., 1980.
Web. doi:10.1103/PhysRevD.21.2047.

```
Bowen, J.M., & York, J.W. Jr..
```*Time-asymmetric initial data for black holes and black-hole collisions*. United States. doi:10.1103/PhysRevD.21.2047.

```
Bowen, J.M., and York, J.W. Jr.. Tue .
"Time-asymmetric initial data for black holes and black-hole collisions". United States. doi:10.1103/PhysRevD.21.2047.
```

```
@article{osti_5392738,
```

title = {Time-asymmetric initial data for black holes and black-hole collisions},

author = {Bowen, J.M. and York, J.W. Jr.},

abstractNote = {As a first step in constructing initial data for dynamic black holes and general black-hole collisions, we study nonsingular vacuum Cauchy hypersurfaces with two isometric asymptotically flat ends connected by an Einstein-Rosen-type bridge. These hypersurfaces are assumed to be conformally flat and maximally embedded in space-time but are neither spherically symmetric nor time symmetric. Three of the four constraints are solved explicitly for suitable extrinsic curvature tensors that possess linear momentum and/or intrinsic angular momentum. The complete initial data are shown to transform invariantly, modulo the sign of the extrinsic curvature tensor, under inversion through a minimal two-surface that represents the ''throat'' of the geometry. These and other properties show that the data represent a particular epoch in the history of a dynamic black hole. We describe the relation of our data to that of the Schwarzschild and Kerr black holes. Finally, we discuss the generalization to encounters of two or more black holes.},

doi = {10.1103/PhysRevD.21.2047},

journal = {Phys. Rev., D; (United States)},

number = ,

volume = 21:8,

place = {United States},

year = {1980},

month = {4}

}