Black brane
Extended, translationally symmetric solution of Einstein field equations.
In general relativity, a black brane is a type of solution to the Einstein field equations. It extends the concept of a black hole by adding p extra spatial dimensions, along which it is extended and translationally symmetric; such a solution is specifically called a black p-brane. In string theory, the term refers to a collection of D1-branes enclosed by a horizon. Because a black hole can be thought of as a zero-brane, a black p-brane is a higher-dimensional generalization. However, many physicists treat black branes as distinct from black holes, noting that a black brane's singularity is not a point but an extended object of higher dimension. A BPS black brane is analogous to a BPS black hole; both carry electric charges, and some BPS black branes also carry magnetic charges.
\[ ds^2 = \left( \eta_{ab} + \frac{r_s^{n-p-3}}{r^{n-p-3}} u_a u_b \right) d\sigma^a d\sigma^b + \left(1 - \frac{r_s^{n-p-3}}{r^{n-p-3}}\right)^{-1} dr^2 + r^2 d\Omega_{n-p-2}^2 \]
Here, \(\eta\) is the \((p+1)\)-dimensional Minkowski metric with signature \((-, +, +, +, \dots)\); \(\sigma\) are the coordinates on the worldsheet of the black p-brane; \(u\) is its four-velocity; \(r\) is the radial coordinate; and \(\Omega\) is the metric for an \((n-p-2)\)-sphere surrounding the brane.
Regarding curvatures, when the metric takes the form \(ds^2 = g_{\mu\nu} dx^\mu dx^\nu + d\Omega_{n+1}\), the Ricci tensor becomes:
\[ R_{\mu\nu} = R^{(0)}_{\mu\nu} + \frac{n+1}{r} \Gamma^r_{\mu\nu}, \qquad R_{ij} = \delta_{ij} g_{ii} \left( \frac{n}{r^2} \dots \right) \]
- Field
- General relativity, string theory
- Known for
- Generalizing black hole solutions with extended spatial dimensions
- Type
- Theoretical object
Lore & Background
In general relativity, a black brane is a solution of the Einstein field equations that generalizes a black hole solution but is also extended—and translationally symmetric—in p additional spatial dimensions. That type of solution would be called a black p-brane. In string theory, the term black brane describes a group of D1-branes that are surrounded by a horizon. With the notion of a horizon in mind as well as identifying points as zero-branes, a generalization of a black hole is a black p-brane. However, many physicists tend to define a black brane separate from a black hole, making the distinction that the singularity of a black brane is not a point like a black hole, but instead a higher dimensional object.
Reader's Guide
A BPS black brane is similar to a BPS black hole. They both have electric charges. Some BPS black branes have magnetic charges. The metric for a black p-brane in an n-dimensional spacetime is given by a specific formula involving the (p+1)-Minkowski metric, coordinates for the worldsheet, four-velocity, radial coordinate, and the metric for an (n-p-2)-sphere surrounding the brane. Curvature quantities such as the Ricci tensor and Ricci scalar for such spacetimes can be expressed in terms of the metric components and Christoffel symbols. The concept of black branes extends the idea of black holes to higher-dimensional objects, with implications for understanding gravity and string theory.
Did You Know?
- A black brane generalizes a black hole solution but is extended and translationally symmetric in p additional spatial dimensions.
- In string theory, a black brane describes a group of D1-branes surrounded by a horizon.
- Many physicists distinguish a black brane from a black hole because its singularity is a higher-dimensional object, not a point.
- Some BPS black branes have magnetic charges, in addition to electric charges.
Frequently Asked Questions
What is a black brane?
A black brane is a theoretical solution to the Einstein field equations that stretches across p additional spatial dimensions beyond the usual three. Unlike a point-like black hole, it is translationally symmetric along those extra directions, making it a higher-dimensional generalization of the standard black hole concept.
How does a black brane differ from a regular black hole?
While a black hole can be viewed as a zero-brane with a localized singularity, a black p-brane extends along p extra spatial dimensions, giving it an elongated or planar geometry rather than a spherical one. Many physicists treat them as fundamentally distinct objects because the singularity structure and horizon shape differ in kind, not just in size.
What does the 'p' in black p-brane refer to?
The letter p counts the number of extra spatial dimensions along which the brane is stretched and symmetric. For instance, a black 1-brane (sometimes called a black string) extends along one additional direction, while a black 2-brane (or black plane) spans two.
What role do black branes play in string theory?
In the string-theory setting, a black brane specifically describes a collection of D1-branes sitting behind a shared event horizon. This makes it a natural object for exploring how extended brane configurations can reproduce gravitational behavior within higher-dimensional frameworks.
Are black branes real physical objects we could observe?
No; black branes remain purely theoretical constructs used by physicists to probe the mathematics of general relativity and string theory. They have never been detected and exist only as exact solutions to field equations in models that posit extra spatial dimensions.
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