The BTZ Format Calculator is an innovative tool designed to simplify complex calculations related to the BTZ (Banados-Teitelboim-Zanelli) black hole, a solution of the (2+1)-dimensional gravity with a negative cosmological constant. This calculator allows users, ranging from students to researchers in theoretical physics, to quickly compute essential properties of the BTZ black hole, such as its mass, based on specific input parameters.

## Purpose and Functionality

The primary objective of the BTZ Format Calculator is to calculate the desired output (such as the mass of a BTZ black hole) based on three input parameters: the AdS (Anti-de Sitter) length scale (l), the outer horizon radius (r+), and the gravitational constant in (2+1) dimensions (G). The calculator uses a specific formula to determine the result:

=2+2*M*=*Gr*+2*l*2

This formula represents the mass *M* of a BTZ black hole in terms of its outer horizon radius +*r*+, the AdS length scale *l*, and the gravitational constant *G* in (2+1) dimensions.

## Step-by-Step Example

Let’s walk through an example calculation using the BTZ Format Calculator:

**Input Parameters**:- AdS length scale (
*l*): 1.0 (arbitrary units) - Outer horizon radius (+
*r*+): 2.0 (arbitrary units) - Gravitational constant (
*G*): 0.1 (in (2+1) dimensions)

- AdS length scale (
**Calculation**: Substituting these values into the formula, we get:=1.020.1×2.02=10.4=2.5*M*=0.1×2.021.02=0.41=2.5**Result**: The mass of the BTZ black hole, based on the given inputs, is calculated to be 2.5 in the chosen units.

## Relevant Information Table

Here’s a table summarizing the inputs and the formula used in the BTZ Format Calculator:

Input Parameter | Symbol | Description |
---|---|---|

AdS length scale | l | The characteristic length scale of the AdS space |

Outer horizon radius | +r+ | Radius of the black hole’s outer event horizon |

Gravitational constant | G | Gravitational constant in (2+1) dimensions |

**Formula**: =2+2*M*=*Gr*+2*l*2

## Conclusion

The BTZ Format Calculator is a powerful and user-friendly tool that significantly eases the calculation of BTZ black hole properties. By providing a simple interface for inputting three key parameters, it enables quick and accurate computations that are essential for students, educators, and researchers in the field of theoretical physics. The calculator not only saves time but also helps in understanding the underlying physics by facilitating the exploration of how different parameters affect the BTZ black hole’s properties. Its application extends beyond educational purposes, serving as a practical tool in research related to quantum gravity and black hole physics.