# Effective Potential of a Black Hole Metric

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This Demonstration shows the effective potential of a black hole of given mass and charge as a function of the radius. The variable gives null paths for the value 0 and time-like paths for the value 1. If the angular momentum is zero, then by setting , the effective potential is the negative of the time component of the diagonal metric tensor.

Contributed by: Timofei Petoukhov (November 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The formula explored is .

The convention of the cosmological constant is chosen to be two times larger than conventional in most literature on the topic. The effective potential is used in the geodesic equation, which is derived from minimizing the action of the path length given some metric.

## Permanent Citation

"Effective Potential of a Black Hole Metric"

http://demonstrations.wolfram.com/EffectivePotentialOfABlackHoleMetric/

Wolfram Demonstrations Project

Published: November 1 2013