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Black hole calculator (Hawking)

hawking_black_hole
Read-onlyIdempotent

Compute a black hole of any mass: event-horizon radius, Hawking temperature, entropy and evaporation time. Use it for physics questions about black holes; give exactly one of mass_kg, mass_solar or preset. Exact formulas, computed locally, no network call.

Input Schema

NameRequiredDescriptionDefault
presetNoKnown object: asteroid, moon, earth, sun, cygnus-x-1, sagittarius-a, m87.
mass_kgNoMass in kilograms (1e3 to 1e45).
mass_solarNoMass in solar masses (1e-25 to 1e12).

Output Schema

NameRequiredDescriptionDefault
citationsYes
provenanceYes
horizon_radius_mNo
hawking_temperature_kNo
evaporation_time_yearsNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed4 schema fields changed
    • addedInput schema / properties / mass_kg / description
      Added value: +"Mass in kilograms (1e3 to 1e45)."
    • addedInput schema / properties / mass_solar / description
      Added value: +"Mass in solar masses (1e-25 to 1e12)."
    • addedInput schema / properties / preset / description
      Added value: +"Known object: asteroid, moon, earth, sun, cygnus-x-1, sagittarius-a, m87."
    • addedOutput schema / description
      Added value: +"Returns mass_kg, mass_solar, horizon_radius_m, hawking_temperature_k, entropy_over_kb, radiated_power_w, evaporation_time_years, evaporating_today."
  2. Added

TDQS

A4.5/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly, idempotent, non-destructive and closed-world; the description reinforces the last point with 'computed locally, no network call' and 'exact formulas', which sets the expectation of deterministic, precise numeric output. It does not describe error behavior when zero or multiple mass inputs are supplied, which is the one genuinely useful disclosure missing.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Two sentences: outputs first, then usage and the one-of constraint. Zero filler and nothing important is buried.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With an output schema present, the description need not explain return values, and it already names the four computed quantities at a summary level. Combined with full schema coverage and annotation-backed safety profile, an agent has everything needed to call it correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the baseline is 3, but the description adds a real constraint the schema does not express: the schema marks nothing as required, yet the tool needs exactly one mass input. That one-of rule is genuinely new information for correct invocation.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb ('compute') and resource ('black hole of any mass') and enumerates exactly what is returned: event-horizon radius, Hawking temperature, entropy, evaporation time. It is clearly distinguishable from astronomy siblings like asteroid_impact or drake_equation.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

'Use it for physics questions about black holes' gives clear usage context, and the selection rule ('give exactly one of mass_kg, mass_solar or preset') covers the main invocation ambiguity. No explicit when-not or named alternative, but no sibling plausibly competes for this task, so the gap is minor.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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